Mikel Arteta believes that Arsenal's Champions League hopes will be decided by the capacity to hold their nerve and be ruthless, as he assessed the suffocatingly tight capital city battle with Chelsea and Tottenham Hotspur over the season's final three weeks.

Arsenal's 1-1 home draw against the newly crowned champions Manchester United on Sunday extended their unbeaten run to seven Premier League matches and it was considered, in all quarters of the club, to have been a good result, even though it meant that they no longer had control of their top-four destiny.

If Tottenham were to win each of their remaining four fixtures, including the one at Chelsea on Wednesday week, and Chelsea were not to drop any points in their other three matches, then Arsenal would finish outside of the Champions League places, irrespective of how they fared in their remaining games against Queens Park Rangers, Wigan Athletic and Newcastle United.

Nobody at Arsenal, from the manager Arsène Wenger down, appears to believe that the nightmare scenario will play out. There is the conviction that, at the very least, Chelsea will not win at United on Sunday and/or Tottenham will not enjoy victory at Stamford Bridge. It might go some way to explaining why the team seemed content to play out the draw in the second half against United.

The focus at Arsenal has turned inwards, with Arteta determined to see his team-mates thrive on the pressure and rise to the occasion. "It will come down to nerve and be about who is the most clinical at the right moments," the midfielder said. "When it gets to the last games, the teams who are the most clinical win. We have seen that over the last few weeks. It will be a battle for everyone. There is pressure on us like there is for the other teams. Every team in the Premier League is playing for something – relegation or Europe. It will be interesting."

Arsenal's run-in would appear favourable, with QPR having had their relegation confirmed and Wigan coming to the Emirates Stadium three days after their FA Cup final against Manchester City. But Wigan will be fighting to preserve their Premier League status and Newcastle could yet be too, which would make Arsenal's last-day trip to St James' Park daunting.

"I believe in our players but we have to show we can do it," Arteta said. "It is easy saying we have a better chance but it is up to us to do it on the pitch. Every game is difficult and anything can happen. We have to play for that."

Arteta believes that United's firepower up front has been the decisive factor this season. Whereas Arsenal, Chelsea and Tottenham have each got two recognised strikers in their squads, United's quartet of Robin van Persie, Wayne Rooney, Javier Hernández and Danny Welbeck have given them the edge. Manchester City blur the lines of the argument slightly, although they sold their fourth striker, Mario Balotelli, to Milan in January. Arsenal now need something out of Lukas Podolski, with Olivier Giroud having begun a three-game suspension against United.

"The difference between United and the rest is that they have four top strikers," Arteta said. "Look at their goal difference. Lukas Podolski has scored a few goals and in front of goal he is the most prolific player we have. It is up to us to get him the chances. He has an unbelievable shot and, hopefully, he can do it for us."